2-regularity

Covering for Set-Valued Mappings in the Absence of Metric Regularity

  • Mario Jelitte
  • Alexey F. Izmailov
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization, Nonsmooth Optimization Tags , , , , ,

    Covering properties build the foundation of stability and sensitivity analysis of solutions to a generalized equation and more specific optimization-related stationarity and equilibrium problems. It has been well-understood that metric regularity of the mapping defining the generalized equation is a key to furnish Lipschitzian stability of the solution of interest. With this work, we want … Read more

    Behavior of Newton-type methods near critical solutions of nonlinear equations with semismooth derivatives

  • Andreas Fischer
  • Alexey F. Izmailov
  • Mario Jelitte
    • Categories Nonlinear Optimization, Nonsmooth Optimization Tags , ,

    Having in mind singular solutions of smooth reformulations of complementarity problems, arising unavoidably when the solution in question violates strict complementarity, we study the behavior of Newton-type methods near singular solutions of nonlinear equations, assuming that the operator of the equation possesses a strongly semismooth derivative, but is not necessarily twice differentiable. These smoothness restrictions … Read more